9.6. Refer to Table 9.5 on the clinical trial for insomnia patients.

(a) To compare effects while controlling for the initial response, add an interaction term to model (9.2). Summarize how the estimated treatment effect varies according to the initial responses by showing that the estimated treatment log odds ratio changes from 0.00 to 1.41 as the initial response score goes from 10 to 75.

(b) Now treat the initial response as qualitative, using indicator variables.

Fit the model without interaction. Show that the estimated treatment log odds ratio is 0.911 (SE = 0.249), and interpret. Now fit the model with interaction terms. Explain why the results suggest that the active treatment seems relatively more successful at the two highest initial response levels.

(c) Using ML or GEE, fit a marginal model for time to fall asleep, with predictors the treatment, the occasion, and treatment x occasion interaction.

Interpret results.